8. Suppose we have a normal distribution of data whose mean is 60 and standard deviation is 10. What is the probability that a data point chosen at random from the dataset will be between the values of 35 and 45? Homework # 2 Biostatistics CLS 603 9. Suppose we have data for a population and we know that the distribution is normal, the mean of the data is 100 and the standard deviation is 15. Find the percentage of data values that lie within 1.5 standard deviation of the mean 10.Suppose one sample of n=36 yields the sample mean X =20 and a sample standard deviation s=4. a. What is the 90% confidence interval for the population mean? b. What is the 95% confidence interval for the population mean? c. What is the 99% confidence interval for the population mean? 11. The housing department in a large city monitors the rent for rent-controlled apartments in the city. The mayor wants an estimate of the average rent. Th housing department must determine the number of apartments to include in asurvey in order to be able to estimate the average rent to within $100 using a 95% confidence interval. From past surveys, the monthly charge for rent- controlled apartments ranged from $1000 to $3600. How many renters must be included in the survey to meet the requirements? 12. Face masks used by firefighters often fail by having their lenses fall out when exposed to very high temperatures. A manufacturer of face masks claims that for its masks the average temperature at which pop-out occurs is 550 F. A sample of 75 masks is tested, and the average temperature at which the lenses popped out was 470 F. Suppose an estimate of o is 0.7 a. If the level of confidence remains 99% but the desired width of the interval is reduced to 0.3, what is the necessary sample size? b. If the level of confidence is reduced to 95% but the desired width of the interval remains 0.5, what is the necessary sample size?… Show more MathStatistics and Probability
